Question

The figure below shows the top view of a circular room with a circular stage. The diameter of the stage is 24 feet. The shaded portion represents the seating for the audience around the stage.

[Use pi = 22/7]

What is the area of the seating portion?

6438.49 ft2

7262.71 ft2

6067.63 ft2

7389.82 ft2

Answer 1

@jim_thompson5910

Answer 2

First you have to find the area of the ring

Area of the ring = (Area of Outer Circle) - (Area of Inner Circle)

Answer 3

Area of the ring = (Area of Outer Circle) - (Area of Inner Circle)

Area of the ring = (pi*50^2) - (pi*12^2)

Area of the ring = 2500pi - 144pi

Area of the ring = 2356pi

Answer 4

ok

Answer 5

Then you have to subtract off those non-shaded pie wedges

Answer 6

Area of pie wedge for the ring = (Area of large pie wedge) - (Area of small pie wedge)

Area of pie wedge for the ring = ((65/360)*pi*50^2) - ((65/360)*pi*12^2)

Area of pie wedge for the ring = 451.3888pi - 26pi

Area of pie wedge for the ring = 425.3888pi

Answer 7

now subtract the two

2356pi - 425.3888pi = 1930.6112pi = 6,065.1939

which is pretty close to 6067.63 (just had some rounding errors)

Answer 8

oh wait, you use pi = 22/7 and not pi = 3.14

so 1930.6112(22/7) = 6,067.6352

Answer 9

which is much closer

Answer 10

thank you very much. i might need your help with just one more problem later. thank you very much! :)